Some Results Concerning Convergence of Convolution Products of Probability Measures on Discrete Semigroups

Abstract

Two types of conditions have been significant when considering the convergence of convolution products of nonidentical probability measures on groups and semigroups. The essential points of a sequence of measures have been useful in characterizing the supports of the limit measures. Also, enough mass eventually on an idempotent has proven sufficient for convergence in a number of structures. In this paper, both of these types of conditions are analyzed in the context of discrete non-abelian semigroups. In addition, an application to the convergence of nonhomogeneous Markov chains is given.